Test: Linear Equations- 1 - Class 8 MCQ

Seven pieces consist of 6 smaller equal pieces and one half cake piece.
Weight of each small piece = 20 gm
So, total weight of the cake = (20×6) = 120gm.
If one half is 120 gm, then so is the other. Therefore the total weight of the cake is 120*2= 240 gm.

Given, 2x - 3 = x + 2
Transposing 'x' to L.H.S
⇒ 2x - x - 3 = 2
⇒ x - 3 = 2
Transposing '3' to R.H.S
⇒ x = 2 + 3
⇒ x = 5.
Therefore, option (b) is the correct answer.

Given equation is 5x−2(2x−7) = 2(3x−1)+7/2

after opening the brackets
5x-4x+14 = 6x-2+7/2
taking x to one side constants to other side
6x+4x-5x=14+2-7/2
or 5x = 16-7/2
or 5x = (32-7)/2
or 5x = 25/2
or x = 25/10
or x = 5/2 (answer)

Given, 2x-3=7
Transposing -3 to R.H.S
2x=7+3
⇒ 2x=10
Transposing '2' to R.H.S, we get
x=10/2
⇒ x=5.
Therefore, the correct option is c.

Let the unit digit be x
Tens digit =  x+3
Therefore, the number formed = 10(x+3)+x ∵ Two digit no = 10 * tens digit + unit digit

 When digits are interchanged i.e
Unit digit = x+3
Tens digit = x
Therefore, the number formed by interchanging the digits is
10x + x + 3
Now, According to question

⇒ 10 (x+3) + x + 10x + x + 3  =143
⇒  10x + 30 + 12x + 3 = 143
⇒  22x + 33 = 143
Transposing '33' to R.H.S, we get
22x = 143−33
⇒ 22x=110
Transposing '22' to L.H.S, we get
 x=110/22
⇒ x=5

Therefore, Original number = 10(5+3) + 5 = 85

Given, 2y + 9 =4
Transposing '9' to R.H.S, we get
2y = 4-9
⇒ 2y = -5
Therefore, y = -5/2
Hence, option 'A' is correct.

Let the two given numbers be 5x and 2x
According to question ,
5x - 2x = 66
3x = 66
Transposing '3' to R.H.S, we get
x = 66/3
⇒ x = 22

So, 2x = 2 x 22 = 44
& 5x = 5 x 22 = 110

Hence, Option 'C' is the Correct answer. 

An algebraic equation is an equality that involves variables. It states that two expressions are equal to each other, typically connected by an equals sign =. For example, in the equation 2x+3=7, the expression 2x+3 is equal to 7. The equation shows the relationship between the variable x and the constants.

Given, 3x = 12
Transposing '3' to R.H.S, we get
x = 12/3
⇒ x = 4

or
Divide both sides by '3' to get the value of x
3x/3 = 12/3 
⇒ x = 4

We have 4x + 5 = 9
⇒ 4x = 9 – 5 (Transposing 5 to RHS)
⇒ 4x = 4
⇒ x = 1 (Transposing 4 to RHS)